Biomedical subjects
Publications and source records attributed to Y S Kivshar.
We study in detail the interaction of composite solitary waves and consider, as an example, the breather collisions in a weakly discrete sine-Gordon equation. We reveal a physical mechanism of fractal soliton scattering associated with multiparticle effects, and demonstrate chaotic interaction of two breathers with incommensurable frequencies.
We develop a theory of modulational instability of multiparameter solitary waves and analyze the transverse instability of composite (or vector) optical solitons in a saturable nonlinear medium. We demonstrate theoretically and experimentally that a soliton stripe breaks up into an array of ( 2+1)-dimensional dipole-mode vector solitons, thus confirming the robust nature of those solitons as fundamental composite structures of incoherently coupled fields.
We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized state, and also reveal a generic physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.
We study linear and nonlinear wave scattering by an optical vortex in a self-defocusing nonlinear Kerr medium. In the linear case, we find a splitting of a plane-wave front at the vortex proportional to its circulation, similar to what occurs in the scattered wave of electrons for the Aharonov-Bohm effect. For larger wave amplitudes, we study analytically and numerically the scattering of a dark-soliton stripe (a nonlinear analog of a small-amplitude wave packet) by a vortex and observe a significant asymmetry of the scattered wave. Subsequently, a wave-front splitting of the scattered wave develops into transverse modulational instability, "unzipping" the stripe into trains of vortices with opposite charges.
We introduce novel classes of optical vector solitons that consist of incoherently coupled self-trapped "necklace" beams carrying zero, integer, and even fractional angular momentum. Because of the stabilizing mutual attraction between the components, such stationary localized structures exhibit quasistable propagation for much larger distances than the corresponding scalar vortex solitons and expanding scalar necklace beams.
We predict the existence of stable nonlinear localized modes near the band edge of a two-dimensional reduced-symmetry photonic crystal with a Kerr nonlinearity. Employing the technique based on the Green function, we reveal a physical mechanism of the mode stabilization associated with the effective nonlinear dispersion and long-range interaction in the photonic crystals.
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of nonlinear impurity modes, one- and two-hump symmetric localized modes and asymmetric localized modes, for both focusing and defocusing nonlinearity and two different (attractive or repulsive) types of impurity. We obtain an analytical stability criterion for the nonlinear localized modes and consider the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site.
We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi(2)) nonlinear interfaces embedded in a linear layered structure--a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi(2) equations) and find, numerically and analytically, the spatially localized solutions--discrete gap solitons. For a single nonlinear interface in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media.
We demonstrate an important role of the process of optical rectification in the theory of nonlinear wave propagation in quadratically nonlinear [or chi(2)] periodic optical media. We derive a novel physical model for gap solitons in chi(2) nonlinear Bragg gratings.
We analyze the transverse instability of two-component spatial solitons in a saturable nonlinear medium, in relation to recent experimental observations of spatial vector solitons in photorefractive media. We present the stability analysis for all three realizations: dark-bright, bright-bright, and dark-dark soliton pairs, and demonstrate that both the nonlinearity saturation and incoherent mode interaction can lead to a strong suppression of the soliton transverse instabilities.
We analyze second-harmonic generation (SHG) at a thin effectively quadratic nonlinear interface between two linear optical media. We predict multistability of SHG for both plane and localized waves, and also describe two-color localized photonic modes composed of a fundamental wave and its second harmonic coupled together by parametric interaction at the interface.
We introduce the concept of two-color multistep cascading for vectorial parametric wave mixing in optical media with quadratic (second-order or chi(2)) nonlinear response. We demonstrate that the multistep cascading allows light-guiding-light effects with quadratic spatial solitons. With the help of the so-called "almost exact" analytical solutions, we describe the properties of parametric waveguides created by two-wave quadratic solitons.